The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 4 (1992), 2100-2110.
Invariant Directional Orderings
Statistical concepts of order permeate the theory and practice of statistics. The present paper is concerned with a large class of directional orderings of univariate distributions. (What do we mean by saying that a random variable $Y$ is larger than another random variable $X$?) Attention is restricted to preorders that are invariant under monotone transformations; this includes orderings such as monotone likelihood ratio, hazard ordering, and stochastic ordering. Simple characterizations of these orderings are obtained in terms of a maximal invariant. It is shown how such invariant preorderings can be used to generate concepts of $Y_2$ being further to the right of $X_2$ than $Y_1$ is of $X_1$.
Ann. Statist., Volume 20, Number 4 (1992), 2100-2110.
First available in Project Euclid: 12 April 2007
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Lehmann, E. L.; Rojo, J. Invariant Directional Orderings. Ann. Statist. 20 (1992), no. 4, 2100--2110. doi:10.1214/aos/1176348905. https://projecteuclid.org/euclid.aos/1176348905